Compound Interest for annuities
Some scheme requires regular deposit for higher interest. These
regular deposits may be at start of year or end of year. Compound interest on this
interest may be worked out by two method i.e. formula and details working.
Example of advance Deposit
|
Investment
|
3,000
|
|
Years
|
3
|
|
Deposit Start of the years
|
|
|
Interest Rate
|
6%
|
Calculate the
future value
Solution
1.
First Method
|
Year 1
|
3,000 x ( 1+.06)3
|
3573
|
|
Year 2
|
3,000 x ( 1+.06)2
|
3371
|
|
Year 3
|
3,000 x ( 1+.06)1
|
3180
|
|
|
|
10,124
|
|
|
|
|
2.
Alternate Methods
= P [ (1+i)n+1-1]-1
I
= 3,000 [3.374]
= $ 10,124
Example of Arrears Deposit
|
Investment
|
3,000
|
|
Years
|
3
|
|
Deposit at year end
|
|
|
Interest Rate
|
6%
|
Calculate the
future value
Solution
3.
First Method
|
Year 1
|
3,000 x ( 1+.06)2
|
3,371
|
|
Year 2
|
3,000 x ( 1+.06)1
|
3,180
|
|
Year 3
|
3,000
|
3,000
|
|
|
|
9,550
|
|
|
|
|
4.
Alternate Method (by formula)
= P [ (1+i)n-1]
I
= 3,000 [3.1836]
= $ 9,550
